Nil restricted Lie algebras of oscillating intermediate growth

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorPetrogradsky, Victor-
Data de aceite: dc.date.accessioned2024-10-23T15:50:06Z-
Data de disponibilização: dc.date.available2024-10-23T15:50:06Z-
Data de envio: dc.date.issued2022-05-23-
Data de envio: dc.date.issued2022-05-23-
Data de envio: dc.date.issued2021-12-14-
Fonte completa do material: dc.identifierhttps://repositorio.unb.br/handle/10482/43775-
Fonte completa do material: dc.identifierhttps://doi.org/10.1016/j.jalgebra.2021.09.003-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/893189-
Descrição: dc.descriptionThe research is motivated by a construction of groups of oscillating growth by Kassabov and Pak [25] and a description of possible growth functions of finitely generated associative algebras by Bell and Zelmanov [9]. In this paper we address both, the question of possible growth functions in case of Lie algebras, and the Kurosh problem, because our examples of restricted Lie algebras have a nil p-mapping, which is an analogue of nillity for associative algebras or periodicity for groups. Namely, for any field of positive characteristic, we construct a family of 3-generated restricted Lie algebras of intermediate oscillating growth. We call them Phoenix algebras because, for infinitely many periods of time, the algebra is “almost dying” by having a quasi-linear growth, namely the lower Gelfand-Kirillov dimension is one, more precisely, the growth is of type , where , are constants. On the other hand, for infinitely many n the growth function has a rather fast intermediate behavior of type , λ being a constant determined by characteristic, for such periods the algebra is “resuscitating”. Moreover, the growth function is bounded and oscillating between these two types of behavior. These restricted Lie algebras have a nil p-mapping, thus addressing the Kurosh problem as well.-
Publicador: dc.publisherElsevier-
Relação: dc.relationhttps://www.sciencedirect.com/science/article/pii/S0021869321004324?via%3Dihub-
Direitos: dc.rightsAcesso Restrito-
Palavras-chave: dc.subjectÁlgebra-
Palavras-chave: dc.subjectLie, Álgebra de-
Palavras-chave: dc.subjectP-grupos-
Palavras-chave: dc.subjectProblema Kurosh-
Título: dc.titleNil restricted Lie algebras of oscillating intermediate growth-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional – UNB

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